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Absorption laws

where and are two-place operations on some set . If these operations satisfy also the laws of commutativity and associativity, then the relation defined by the equivalence

(*)

(or equivalently, by the equivalence ) is an order relation for which is the infimum of the elements and , while is the supremum. On the other hand, if the ordered set contains an infimum and a supremum for any pair of elements and , then for the operations and the laws of absorption, commutativity and associativity, as well as the equivalence (*) apply.